Evaluate Returns

Overview

• Suppose we’ve run a backtest and saved the portfolio returns.
• Evaluate raw returns: accumulation, drawdowns, mean, std dev, Sharpe ratio
• Evaluate relative to benchmarks
  • Compare to the market on a beta-adjusted basis
  • Compare to the market and other factors (attribution analysis)

Drawdowns

• A drawdown occurs whenever your portfolio value is not as high as it once was
• The percent drawdown is (current value - prior max) / prior max.

Statistics

• mean and std dev of monthly returns
• annualize mean by \(\times\) 12
• annualize std dev by \(\times\) sqrt(12)
• compute monthly excess returns (in excess of T-bill rate), mean and std dev and Sharpe ratio = mean / std dev
• annualize Sharpe ratio by \(\times\) sqrt(12)

Example accumulation plot

(1+ret).cumprod().plot()
(1+mkt).cumprod().plot()

Example drawdown plot

accum = (1+ret).cumprod()
accum_max = accum.expanding().max()
drawdown = accum/accum_max - 1